# packages
library(tidyverse)
library(googlesheets4)
library(here)
library(metafor) 
library(metaAidR) # see a note above
library(orchaRd) # see a note above
library(ape)
library(clubSandwich)
library(metaAidR)
library(patchwork)
library(emmeans) # see a note above
library(kableExtra)
library(GGally)
library(cowplot)
library(grDevices) # reqired for using base and ggplots together

# Below is the custom function to calculate the lnRR 
lnRR_func <- function(Mc, Nc, Me, Ne, aCV2c, aCV2e, rho = 0.5){
  lnRR <- log(Me/Mc) + 
        0.5 * ((aCV2e/Ne) - (aCV2c/Nc)) 
  
  var_lnRR <- (aCV2c/Nc) + (aCV2e/Ne) - 
         2 * rho * ((aCV2c*aCV2e)/sqrt(Nc*Ne)) 
  
  data.frame(lnRR,var_lnRR)
}

# Mc: Concentration of PFAS of the raw (control) sample
# Nc: Sample size of the raw (control) sample
# Me: Concentration of PFAS of the cooked (experimental) sample
# Ne: Sample size of the cooked (experimental) sample 
# aCV2c: Mean coefficient of variation of the raw (control) samples
# aCV2e: Mean coefficient of variation of the cooked (experimental) samples